Wayne needs to drive 470 miles to reach Milwaukee. Suppose he drives at a constant speed of 50 miles per hour. Which function represents Wayne’s distance in miles from Milwaukee in terms of the number of hours he drives?

y = 420x

y = 470 + 50x

y = 50 − 470x

y = 50 + 470x

y = 470 − 50x

The correct answer is [tex]\sum_{n=1}^{20} (-8 + 5(n-1))[/tex]

The sum using summation notation, assuming the suggested pattern continues, can be written as:

[tex]\sum_{n=1}^{20} (-8 + 5(n-1))[/tex]

[tex]-8 - 3 + 2 + 7 + \ldots + 67 = \sum_{n=1}^{20} (-8 + 5(n-1))[/tex]

Explanation:

- The pattern appears to be an arithmetic progression with a common difference of 5.

- The first term is -8, and the common difference is 5.

- The nth term of an arithmetic progression can be expressed as [tex]a_n = a_1 + (n-1)d[/tex], where [tex]a_1[/tex] is the first term, and [tex]d[/tex] is the common difference.

- Substituting [tex]a_1 = -8[/tex] and [tex]d = 5[/tex], we get [tex]a_n = -8 + 5(n-1)[/tex].

- The sum of the first 20 terms of this arithmetic progression can be represented using the summation notation, with the index [tex]n[/tex] ranging from 1 to 20.

Therefore, the sum using summation notation is [tex]\sum_{n=1}^{20} (-8 + 5(n-1))[/tex].

Complete question:

Write the sum using summation notation, assuming the suggested pattern continues.

-8 - 3 + 2 + 7 + ... + 67

summation of the quantity negative eight plus five n from n equals zero to fifteen

summation of negative forty times n from n equals zero to infinity

summation of negative forty times n from n equals zero to fifteen

summation of the quantity negative eight plus five n from n equals zero to infinity

Answer:

Relative frequency, by row, of students who like both tacos and pizza is:

0.81

Step-by-step explanation:

                                  Like Tacos Do Not Like Tacos      Total

Like Pizza                    57                 13                       70

Do Not Like Pizza            12                  15                       27

Total                            69          28                       97

The relative frequency by row is calculated as the ratio of the frequency of the required field to the total frequency of that row

Hence, relative frequency, by row, of students who like both tacos and pizza is:

57/70

=0.81

Answer:

4

Step-by-step explanation:

The value of angle ADB in the triangle ADB is determined as m∠ ADB = 95⁰. (Option A).

How to calculate angle ADB?

The value of angle ADB is calculated by applying intersecting chord theorem and principle of sum of angles in a triangle.

The intersecting chord theorem states that the angle at tangent is half of the arc angle of the two intersecting chords.

So the value of angle A is calculated as follows;

m ∠ BAC = ¹/₂ x arc BC

m ∠ BAC = ¹/₂ x 110

m ∠ BAC  = 55

The value of angle ADB is calculated as follows;

m ∠ ABD + m ∠ ADB + m ∠ BAD = 180 (sum of angles in a triangle)

30 + m ∠ ADB + 55 = 180

m ∠ ADB + 85 = 180

m ∠ ADB = 180 - 85

m ∠ ADB = 95⁰

Answer:

[tex]x=-2,x=2[/tex]

Step-by-step explanation:

we have

[tex]x^{2}+2=6[/tex]

we know that

The solution of the function is equivalent to solve the following system of equations

[tex]y=x^{2}+2[/tex] ------> equation A

[tex]y=6[/tex] ------> equation B

The x-coordinate of the intersection point both graphs is the solution of the given function

Using a graphing tool

see the attached figure

The intersection points are [tex](-2,6)[/tex] and [tex](2,6)[/tex]

therefore

The solution of the given function are

[tex]x=-2,x=2[/tex]

replace y with -3

2y + 7 becomes 2(-3) + 7 = -6 +7 =1

-4(-3)-10 = 12-10 = 2

Final answer:

To convert the chances of a '1 in 19' win into a probability value, you divide 1 by 19 to get 0.05263 and then round to 0.053. Therefore, the lottery win probability is 0.053.

Explanation:

To express the likelihood of a win in a lottery game as a probability value between 0 and 1, when the chances of a win are stated as "1 in 19", you follow these steps:

Understand that "1 in 19" means there is one chance to win for every 19 trials, so the total number of possible outcomes is 19 (18 losses + 1 win).

Express the chance to win as a fraction with the number of wins (1) over the total number of potential outcomes (19).

Convert the fraction into a decimal by dividing the numerator (1) by the denominator (19), which gives you approximately 0.05263.

Round the result to three decimal places, as requested, which gives you a probability value of 0.053.

Therefore, the probability of winning the lottery game is 0.053.

The length of the diagonal of Kit's bandana tied around her head is approximately 22.63 inches long.

Kit folds a bandana diagonally.

To find the length of the diagonal (hypotenuse of a right triangle), we can use the Pythagorean theorem.

The bandana side length (a) is 16 in.

Let x be the length of the diagonal.

Using a^2 + a^2 = x^2, we get 16^2 + 16^2 = x^2. Solving this gives x ≈ 22.63 in.

The area of 13 feet long by 9 feet wide wildflower garden is 117 square feet.

Use the concept of a rectangle defined as:

Rectangles are four-sided polygons with all internal angles equal to 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from a square in that its opposite sides are equal in length.

To find the area of her garden,

Multiply the length and width of the space.

In this case,

the length is 13 feet and the width is 9 feet.

So, the area of Mia's garden would be,

13 feet x 9 feet = 117 square feet.

Hence,

The area of the garden is 117 square feet.

To learn more about rectangles visit:

https://brainly.com/question/15019502

#SPJ5

The normal line to the parabola [tex]y=x-x^2[/tex] at the point [tex](1,0)[/tex] intersect it second time at the point [tex](-1,-2)[/tex].

The given equation is:

at point,

then,

→ [tex]y' = 1-2x[/tex]

So, at (1,0),

→ [tex]y' = 1-2\times 1[/tex]

      [tex]= -1[/tex]

Since,

This is the slope of the tangent, we take its negative reciprocal to get the slope of normal:

= [tex]-\frac{1}{(-1)}[/tex]

= [tex]1[/tex]

The normal line has slope 1 and goes through (1,0):

→ [tex]y-0=1(x-1)[/tex]

→       [tex]y = x-1[/tex]

We want to know where this intersects [tex]y = x-x^2[/tex], we get

→ [tex]x-1=x-x^2[/tex]

→ [tex]x^2=1[/tex]

→ [tex]x = \pm 1[/tex]

hence,

The point corresponding to (1,0) is the one we started with, so we want x=-1:  

→ [tex]x = -1[/tex]

→ [tex]y = x-x^2[/tex]

By substituting the value of "x", we get

→    [tex]= -1-1[/tex]

→    [tex]= -1[/tex]

Thus the answer above is right.

Learn more about Parabola here:

https://brainly.com/question/21685473

The car gets 20 miles per gallon.

To find the miles per gallon the car gets, we need to divide the total miles driven by the number of gallons of gas used. In this case, the car goes 332 miles on a single tank, and the gas tank holds 16.6 gallons. So, the miles per gallon can be calculated as:

Miles per gallon = Total miles driven / Number of gallons used

Miles per gallon = 332 miles / 16.6 gallons

Miles per gallon = 20 miles

Therefore, the car gets 20 miles per gallon.

https://brainly.com/question/37036502

#SPJ2

To find the volume of sand needed for Maija's sandbox, multiply the length, width, and depth. As the sandbox is a square, both the length and width are 3 feet. The depth is 0.85 feet. Thus, Maija needs 7.65 cubic feet of sand.

This question is about calculating volume, specifically the volume of sand that Maija needs for her sandbox. The volume of a box is calculated by the formula: volume = length x width x height. Since the sandbox is square, the length and width are both 3 feet. The height, or in this case, the depth of the sand, is 0.85 feet.

Therefore, the volume of sand needed is calculated as follows: Volume = 3 ft x 3 ft x 0.85 ft = 7.65 cubic feet. So, Maija needs exactly 7.65 cubic feet of sand for her sandbox.

https://brainly.com/question/33318354

#SPJ5

Recognizing the specific forms of square trinomials and the difference of squares allows you to rewrite them as separate factors, simplifying algebraic expressions and facilitating further mathematical operations.

Knowing when to rewrite square trinomials and the difference of squares as separate factors depends on the algebraic expression you are dealing with. Let's consider each case separately.

1. Square Trinomials:

  - Square trinomials have the form [tex]\(a^2 + 2ab + b^2\) or \(a^2 - 2ab + b^2\)[/tex], where(a) and (b) are algebraic expressions.

  - These trinomials can be factored into the square of a binomial: [tex]\((a + b)^2\) or \((a - b)^2\).[/tex]

  - You should rewrite a square trinomial as separate factors when you encounter an expression that matches the form of a perfect square trinomial. Recognizing this pattern allows you to simplify the expression.

2. Difference of Squares:

  - The difference of squares has the form [tex]\(a^2 - b^2\),[/tex] where (a) and (b) are algebraic expressions.

  - This expression can be factored into the product of conjugates: [tex]\((a + b)(a - b)\).[/tex]

  - You should rewrite a difference of squares as separate factors when you have an expression in the form [tex]\(a^2 - b^2\)[/tex]. Recognizing this pattern helps you simplify and factor the expression efficiently.

The diagonals are 3 cms long each. The area of the kite in the given figure is 9 [tex]cm^2[/tex].

Mathematically, a quadrilateral with two pairs of adjacent sides that are congruent (have equal length) is termed a "kite". Note that not all quadrilaterals with congruent adjacent sides are kites. Kites have numerous applications in geometry, including the study of polygons, symmetry, and angles. They can be used to solve geometric problems and to analyze relationships between sides, angles, and diagonals within the quadrilateral.

Given that the length of the diagonals = 3 cm.

It is known that

Area of a quadrilateral with equal diagonals = product of the diagonals.

Area = 3 [tex]\times[/tex] 3.

Area = 9 [tex]cm^2[/tex].

The area of the kite is 9 [tex]cm^2[/tex].

Learn more about kites here:

https://brainly.com/question/32053097

#SPJ4

The complex solutions of x^2+5x-5=0 are (-5 + √45)/(2) and (-5 - √45)/(2).

To find the complex solutions of x2+5x-5=0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac))/(2a)

Substituting the values a=1, b=5, and c=-5 into the formula, we get:

x = (-5 ± √(5^2 - 4(1)(-5)))/(2(1))

Simplifying further,

x = (-5 ± √(25 + 20))/(2)

x = (-5 ± √(45))/(2)

Since the square root of 45 cannot be simplified, we can write the solutions as:

x = (-5 ± √45)/(2)

Therefore, the complex solutions to the equation x2+5x-5=0 are:

x = (-5 + √45)/(2), (-5 - √45)/(2)

https://brainly.com/question/29589619

#SPJ2